Pierre Marchand
Pierre Marchand
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2
High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem
We study a commonly-used second-kind boundary-integral equation for solving the Helmholtz exterior Neumann problem at high frequency, …
Jeffrey Galkowski
,
Pierre Marchand
,
Euan A. Spence
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arXiv
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?
We consider GMRES applied to discretisations of the high-frequency Helmholtz equation with strong trapping; recall that in this …
Pierre Marchand
,
Jeffrey Galkowski
,
Alastair Spence
,
Euan A. Spence
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arXiv
Eigenvalues of the truncated Helmholtz solution operator under strong trapping
For the Helmholtz equation posed in the exterior of a Dirichlet obstacle, we prove that if there exists a family of quasimodes (as is …
Jeffrey Galkowski
,
Pierre Marchand
,
Euan A. Spence
Preprint
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arXiv
Two-level preconditioning for h-version boundary element approximation of hypersingular operator with GenEO
In the present contribution, we consider symmetric positive definite operators stemming from boundary integral equation (BIE), and we …
Pierre Marchand
,
Xavier Claeys
,
Pierre Jolivet
,
Frédéric Nataf
,
Pierre-Henri Tournier
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Boundary integral multi-trace formulations and Optimised Schwarz Methods
In the present contribution, we consider Helmholtz equation with material coefficients being constants in each subdomain of a geometric …
Xavier Claeys
,
Pierre Marchand
Preprint
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